Abstract: We report the discovery of 3.76-s pulsations from a new burst source near Sgr
A* observed by the NuSTAR Observatory. The strong signal from SGR J1745-29
presents a complex pulse profile modulated with pulsed fraction 27+/-3 % in the
3-10 keV band. Two observations spaced 9 days apart yield a spin-down rate of
Pdot = (6.5+/-1.4)x10^{-12}. This implies a magnetic field B = 1.6x10^14 G,
spin-down power Edot = 5x10^33 erg/s, and characteristic age P/2Pdot = 9x10^3
yr, for the rotating dipole model. However, the current Pdot may be erratic,
especially during outburst. The flux and modulation remained steady during the
observations and the 3-79 keV spectrum is well fitted by a combined blackbody
plus power-law model with temperature kT_BB = 0.96+/-0.02 keV and photon index
= 1.5+/-0.4, respectively. The neutral hydrogen column density (nH ~ 1.4x10^23
cm^{-2}) measured by NuSTAR and Swift suggests that SGR J1745-29 is located at
or near the Galactic Center. The lack of an X-ray counterpart in the published
Chandra survey catalog sets a quiescent 2-8 keV luminosity limit of Lx ~< 10^32
erg/s. The bursting, timing, and spectral properties indicate a transient
magnetar undergoing an outburst with 2-79 keV luminosity up to 3.5x10^35 erg/s
for a distance of 8 kpc. SGR J1745-29 joins a growing subclass of transient
magnetars, indicating that many magnetars in quiescence remain undetected in
the X-ray band or have been detected as high-B radio pulsars. The peculiar
location of SGR J1745-29 has important implications for the formation and
dynamics of neutron stars in the Galactic Center region.